Siddig was born in the Sudan and raised there until political turmoil forced his British mother to flee to the U.K. where she sent for him a short time later. His English schooling was financed by his uncle, British actor Malcolm McDowell. Siddig attended university to study geography and anthropology, thinking the future ability to help his native country might lie in the sciences, not on the stage. But during school, he became interested in acting and directing and left university to begin studies at the prestigious London Academy of Music and Dramatic Arts.

Being one of the few trained dramatic actors of Arabic descent in London at the time, he was soon cast as a young Palestinian in the television miniseries, The Big Battalions, which led to his winning role as 'Feisal' in A Dangerous Man: Lawrence After Arabia. That movie was subsequently broadcast on American television and his performance caught the attention of Star Trek producer, Rick Berman. On stage, Siddig co-starred in the London West End production of Whose Life Is It Anyway? with Kim Cattrall.